In addition to Byzantine-robust decentralized stochastic optimization over static networks, we are also interested in the case that the underlying network topologies are time-varying, which finds applications in mobile computation systems and robotic swarms. Various decentralized stochastic optimization algorithms over time-varying networks have been developed, such as those in [1]}, [2]}. Some of the recent works further consider that the time-varying networks are directed such that the designed mixing matrices are column stochastic [3]}, [4]}, [5]} or row stochastic [6]}. However, none of these algorithms take into account the existence of Byzantine agents. On the other hand, there exist other works considering adversarial attacks over time-varying graphs. For example, the works of [7]}, [8]} focus on robust distributed parameter estimation, while their attack model is different from ours. To be specific, the works of [7]}, [8]} consider adversarial attacks on the measured data, while our Byzantine attack model considers attacks during the optimization process.
